understanding ccss and k- 12 instructional shifts in math jamie sirois, cooperative middle school,...
TRANSCRIPT
UNDERSTANDING CCSS AND K-12 INSTRUCTIONAL
SHIFTS IN MATH
Jamie Sirois, Cooperative Middle School, Statham, NH
Adapted From: Maxine Mosely CCRS 101
NH-CCRS CORPS
Agenda:
● Welcome● Common Core State Standards in Theory● What Are the Major Shifts in Math● Common Core State Standards in Practice● Following the Standard from Start to Finish
Who Am I?
Mrs. Jamie L. Sirois, M Ed
• 6th Grade Math Teacher and Learning Area Leader at the Cooperative Middle School in Stratham, NH
• Member of NEA-NH Common Corps • Member of the NH State Consortium on
Educator Effectiveness• Co-Author of “The Everything Parents
Guide to the Common Core Math: Grades 6 – 8”
COMMON CORE STATE STANDARDS IN THEORY
New Hampshire College- and Career-Ready Standards
Knowledge: Refers to mastery of
rigorous content knowledge across
multiple disciplines that serve as a foundation for
all learning.
Skills:Refers to the higher-
order skills that students need in order to extend
and apply rigorous content knowledge.
Work Study Practices:
Refers to socio-emotional skills or
behaviors that associate with success in both college and career.
Rose Colby, presentation to EHS, August 4, 2013
NH-CCRS and Math● Mathematics classes will cover fewer
concepts but in more detail● The focus is on HOW and WHY kids arrive
at an answer so they can apply it to the real world
● Teach less…Learn more● NH-CCRS only identifies what students
should learn, not how teachers should teach
College and Career Readiness Standards in Mathematics
● Students must demonstrate fluency in solving math problems
● Students must provide evidence of their thinking or habits of mind
● Use higher-order thinking
WHAT ARE THE MAJOR SHIFTS WITH CCSS?
Mathematical Shifts
FOCUS
COHERENCE
RIGOR
Focus Strongly Where the Standards Focus
Focus deeply on the standards of each grade so that students can gain:Depth not breadthStrong foundations Solid conceptual understandingA high degree of procedural skill and fluencyThe ability to apply math they know to solve
problems inside and outside the math classroom
CoherenceCOHERENCE: Think across grades, and link to
major topics within gradesThe Standards are designed around coherent
progressions from grade to grade.
The goal is to connect the learning across grades so that students can build new understanding onto
foundations built in previous years. Each standard is not a new event, but an extension of previous learning.
RigorIn major topics, include:
conceptual understanding, procedural skill and fluency, and application with equal intensity
Conceptual Understanding: Teachers support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures
RigorProcedural skill and fluency: Students
have speed and accuracy in calculation
Application: Students use math flexibly and apply math in various contexts
Exploring the Eight Standards for Mathematical Practice
● Make sense of problems and persevere in solving them
● Reason abstractly● Construct viable arguments of others● Model with mathematics● Use appropriate tools strategically● Attend to precision● Look for and make use of structure● Look for and express regularity in repeated
reasoning
COMMON CORE STATE STANDARDS IN PRACTICE
College and Career Ready Standards
Competencies (SAU)
Learning Targets (School & Grade
Level)
Curriculum and Activities
(School & Teacher)
State-Wide Testing
(State Directed)
Classroom Assessments
(School and Teacher)
Learning the Vocabulary• Standards are the overarching learning objectives that we want
students to learn and be able to do.• Curriculum refers to the means and materials with which students will
interact for the purpose of achieving identified educational outcomes.• Activities are the individual lessons and experiences teachers use to
help students learn and master a particular standard and become part of a schools curriculum.
• Assessments are the tools we use to measure a students level of mastery.• Summative Assessments are end of unit assessments• Formative Assessments measure a students progress in meeting the standard
and are used to guide instruction. These are temperature readings along the way.
6th Grade Expressions and Equations:
Apply and extend previous
understandings of arithmetic to algebraic
expressions.CCSS.MATH.CONTENT.6.EE.A.2.A
Example: The cost to go bowling is $7 per game (g) plus $6 to rent a pair of shoes. Write an expression to show the cost per person to go bowling.
Answer: 7g + 6
7th GradeExpressions and Equations:
Solve real-life and mathematical
problems using numerical and algebraic
expressions and equations.CCSS.MATH.CONTENT.7.EE.B.4.A
Example:The number of seventh-grade students that went on the field trip was 4 more than 3 times the number of seventh grade students that went on the same trip last year. If 40 students went on this year’s field trip, what equation can you write to find how many students went last year?
Answer: 3x + 4 = 40So, 12 students went on the field trip last year.
8th GradeExpressions and Equations:
Analyze and solve linear equations and
pairs of simultaneous linear equations.CCSS.MATH.CONTENT.8.EE.C.7.A
Example:Lucinda paid $28 for 3 lbs of cherries and 2 lbs of apples. Her sister paid $17 for 2 lbs of cherries and 1 lb of apples. Solve for the cost of 1 lb of cherries and 1 lb of apples.
3c + 2a = 282c + a = 17
Answer:1 pound of cherries = $6.001 pound of apples = $5.00
Changing Questions to Increase UnderstandingCCSS.MATH.CONTENT.6.NS.B.4Find the greatest common factor of two whole numbers less than or equal to 100 and the least common
multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)..
What is the Greatest Common Factor of 8 and 6?
The Greatest Common Factor of 8 and some number is equal to 2. Find the 5 smallest whole number values for the
missing number. Show your work and explain your process.
�
FOLLOWING A STANDARD FROM START TO FINISH
Common Core State Standard 6.EE.A.3• Apply the properties of operations to generate equivalent
expressions. For example, apply the distributive property to the expressions 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
School Generated Learning Targets• In student friendly language, schools create I can statements:
• I can apply the properties of operations, with a focus on the distributive property, to generate equivalent expressions. • (EX: 3(2 + x) = 6 + 3x
• I can identify when two expressions are equivalent (i.e., when two expressions name the same number regardless of which value is substituted into them).
• I can simplify expressions by combining like terms.• y + y + y = 3y
Teacher Designs an Activity To Engage Students in Learning the Objective
• Starburst Distributing Activity• Refer to handouts.• Distribute Bags of Starbursts to tables…
3(2r + y)
R R Y
R R Y
R R Y
6r + 3y
For this example, students have not been given enough
manipulatives to model this problem. This was done
intentionally to see if they could make the connections with repeated addition and the
distributive property.
12(6p + 8y)
12•6p + 12•8y72p + 12•8y72p + 96y
Activity Leads to Independent Practice
Independent Practice Leads to Assessment
http://tinyurl.com/standardtoassessment
The above link is for our locally designed assessment, created by four 6th grade math teachers at the Cooperative Middle School in Stratham, NH.
Smarter Balanced Assessment Sample Question
